⡒⠐⠂⠒⠐⠂⠂⠀⠀⡰⠒⠒⢆⠀⠰⡒⠒⢲⡀⠀⡴⠒⢒⡖⡒⠂⠒⠀⠀⠀⠀⢀⡤⠒⠉⠉⠑⠢⡀⠀⠀⠐⠐⠂⠒⠒⠢⡄⠀⠀
⠂⠀⡀⠀⠀⠠⠁⠀⢠⠃⠀⠀⠸⡀⠀⠱⡄⠀⢳⡰⠁⠀⡞⠀⡇⠀⢘⠀⠀⠀⢠⠋⠀⢀⣀⢀⡀⠀⠘⣆⠀⠨⠀⢠⠤⣄⠀⠸⡄⠀
⠀⠀⡅⠀⠐⠀⠀⠀⡜⠀⢸⡆⠀⢇⠀⠀⠹⡀⠀⠁⢀⡞⠀⠀⠇⠀⢨⠀⠀⠀⡎⠀⢠⠋⠀⠀⠈⣆⠀⢸⡀⠨⠀⢸⠀⣸⠀⠀⡇⠀
⠀⠀⠆⠀⢈⠀⠀⢠⠃⠀⡇⢱⠀⠸⡄⠀⠀⢱⠀⠀⡜⠀⠀⠀⡃⠀⠰⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⢸⠀⠀⡇⢈⠀⢈⠉⠁⢀⡼⠀⠀
⠀⠀⡃⠀⠠⠀⠀⡜⠀⠘⠓⠚⠂⠀⢣⠀⠀⠠⠀⠀⠇⠀⠀⠀⡅⠀⢘⠀⠀⠀⢇⠀⠘⣄⠀⠀⢀⠏⠀⢸⠁⢘⠀⢸⢆⠀⠳⡀⠀⠀
⠀⠀⡅⠀⠐⠀⢰⠁⠀⡤⠤⠤⢤⠀⠘⡄⠀⠨⠀⠀⡃⠀⠀⠀⠆⠀⠈⠐⠒⢰⠘⣄⠀⠈⠉⠊⠁⠀⢠⠏⠀⢘⠀⢸⠘⡄⠀⠱⡀⠀
⠀⠀⠦⠠⠬⠀⠮⠤⠴⠁⠀⠀⠘⠦⠤⠧⠀⠰⠤⠤⠁⠀⠀⠀⠣⠄⠤⠤⠤⠼⠀⠈⠳⠤⣀⣀⡠⠔⠁⠀⠀⠠⠤⠼⠀⠘⠤⠤⠵⠀
⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡀⠀⢀⣀⣀⣀⠀⠀⢀⣠⣾⢻⣽⢫⣟⢷⣤⡀⠀⠀⢀⣠⠤⠤⢄⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⢸⠀⠀⡎⠀⠀⢹⠀⠀⢣⠀⠈⢆⢀⣾⡟⣞⣟⣞⣟⡾⣫⢾⡵⡄⡴⠋⠀⠀⠀⠀⠈⠳⣠⡚⢮⡒⣆⢄⡀⠈⢳⡀⠀
⠁⠉⡇⠀⢸⠉⠉⠀⢰⠁⠀⡀⠀⡇⠀⠀⢇⠀⠈⣾⡷⢿⣹⣎⣷⣾⡹⣏⢷⡏⣿⠁⠀⣰⠾⠹⢆⠀⠀⣇⠹⣆⢹⡸⣆⣱⠀⠀⡇⠀
⠀⠀⡇⠀⢸⠀⠀⠀⡞⠀⢸⢇⠀⢱⠀⠀⠈⢆⢀⣿⣹⢯⣗⡯⣞⠲⡟⣭⢫⡜⡷⠀⢰⠃⠀⠀⠀⢣⠀⠚⡗⢪⠃⢹⠲⡜⠀⢀⡇⠀
⠀⠀⡇⠀⢸⠀⠀⢰⠃⠀⡇⢸⡀⠈⡇⠀⠀⠈⣾⢧⣟⡾⣺⡕⣎⠳⣍⢖⣣⢚⣽⠀⢸⠀⠀⠀⠀⢸⠀⠀⡇⢸⠀⢠⠟⣜⡣⠞⠀⠀
⠀⠀⡇⠀⢸⠀⠀⡎⠀⠈⠉⠉⠁⠀⢹⠀⠀⣠⣿⣹⢮⢷⡻⡼⣌⠳⡜⡶⣿⣾⣷⠀⠀⠣⣀⣀⡠⠃⠀⢸⠁⢸⠀⢈⡞⡴⣩⣄⠀⠀
⠀⠀⡇⠀⢸⠀⢸⠁⠀⡖⠒⠒⢲⡀⠀⡇⣠⡽⣖⣯⢯⣏⢷⡹⣜⡳⣍⣞⡴⣯⠃⢣⡀⠀⠀⠀⠀⠀⡰⠃⠀⢸⠀⠰⣸⠱⡥⠞⢆⠀
⠀⠀⠓⠒⠚⠀⠓⠒⠚⠀⠀⠀⠀⣗⢲⡹⣾⡟⡜⣎⡻⣞⢧⣛⢶⡹⣽⢞⡽⡽⢤⠄⣉⢒⣤⡤⠔⠊⠀⠀⠀⠘⠒⢺⢥⢳⡙⢾⠚⠂
⡤⠤⠤⠤⠤⠤⢤⠀⠀⢠⠤⠤⡼⣌⠳⡜⣿⡯⡱⣝⡲⣹⢎⡞⢧⠽⣯⢾⣝⡧⣋⠞⣬⢚⡴⡩⢏⡻⣙⠧⣋⢗⡲⡜⡜⢦⡙⣎⡀⠀
⣅⣀⡀⠀⢀⣀⣸⠀⠀⡎⠀⢰⠳⣌⠻⡜⣿⡷⣙⠦⣝⠶⡹⡜⣭⣛⡷⢯⣞⡡⢏⡜⢦⣋⠶⡹⢬⡱⣍⠞⡥⢎⡵⢪⠝⢦⣹⠴⡇⠀
⠀⠀⡇⠀⢸⠈⠈⠀⢸⠁⢠⣞⠳⣌⠳⣽⣿⣿⢵⢫⡜⣭⢳⣙⢦⢻⡽⣏⡾⣇⠯⡜⡣⡼⠒⠩⠶⣵⠮⠾⡥⢫⠂⠉⡏⢹⠀⠀⡇⠀
⠀⠀⡇⠀⢸⠀⠀⠀⡏⠀⡸⣏⠳⣬⢳⣿⢿⣯⣿⣧⣿⢶⣧⣾⣮⡿⣟⣻⢷⣻⠜⠊⢸⠀⠀⠀⠀⢸⠀⠀⡇⢸⠀⠀⠓⠊⠀⢠⠇⠀
⠀⠀⡇⠀⢸⠀⠀⢸⠁⠠⢷⢬⠳⣌⣛⣞⣝⣳⡌⣻⢿⣿⣽⣿⡳⡾⣎⠿⣷⡿⣤⠀⠘⡄⠀⠀⠀⡼⠀⢀⡇⢸⠀⠀⡆⠀⢺⡁⠀⠀
⠀⠀⡇⠀⢸⠀⢀⡇⠀⣀⡞⣬⠳⡜⣬⣿⢿⣙⣿⢿⡿⣿⣺⣿⢟⣬⣧⣿⣗⢿⡘⡄⠀⠈⠒⠴⠊⠁⠀⡼⠀⢸⠀⠀⡟⡄⠀⢳⡀⠀
⠀⠀⣇⣀⣸⠀⣸⣀⣀⡷⣱⠪⢵⣉⣛⣿⣿⡷⣿⣟⣿⣿⣿⣿⡽⣿⣵⡿⣿⣷⠀⠘⠦⣀⠀⠀⢀⣠⠞⠀⠀⢸⣀⣀⡇⠸⣄⣀⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⣱⢃⡛⢦⡍⠀⢙⣿⣿⣿⣿⣿⡿⣽⣽⣿⣿⢿⡿⣿⠁⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⠒⠒⠒⠒⠒⢲⣜⠲⣥⢫⡜⣳⠀⠐⡞⣿⣿⣻⣿⡏⣟⣟⣯⢭⣽⣿⢾⣟⡇⠀⠀⣠⠔⠒⠒⠒⠦⡀⠀⠀⢰⠒⠒⠒⠒⠦⣄⠀⠀
⢰⣀⣀⠀⢀⣀⡸⣌⠳⢆⣳⡌⠘⡆⠀⠘⣯⢿⣿⡽⣽⣻⡿⣼⣿⣷⢿⣿⣯⢞⠀⡞⠁⠀⢀⣀⡀⠀⠈⢇⠀⢸⠀⠀⡤⣀⠀⠈⡆⠀
⠀⠀⡇⠀⢸⢠⢳⡩⡝⢎⢂⡇⠀⢳⠀⠀⢸⣯⣷⣟⡽⣻⣽⢶⣿⣫⢿⣗⣷⡿⢞⡀⠀⡞⠁⠀⠉⢦⠀⠘⡆⢸⠀⠀⡇⢘⠆⠀⡇⠀
⠀⠀⡇⠀⢸⣬⢣⠳⡼⠁⡸⢸⡀⠈⡆⠀⣸⣿⣯⢫⡟⣿⣿⢿⣿⣗⡟⣟⣺⣿⣿⣿⣟⡀⠀⠀⠀⢸⠀⠀⡇⢸⠀⠀⠓⠋⠀⣠⠃⠀
⠀⠀⡇⠀⣜⢦⣋⢵⢁⡀⠓⠒⠃⠀⢹⢠⡿⣿⣻⡿⢿⣿⡝⡿⢻⢻⣿⣯⣿⣿⢿⣿⣿⣿⡀⠀⠀⡼⠀⢀⡇⢸⠀⠀⣇⠀⠹⡁⠀⠀
⠀⠀⡇⢸⢱⣎⢀⣿⣿⣇⣀⣀⣀⠀⠈⣿⣿⣿⣿⣿⡿⡿⣁⠹⡆⣏⣿⣿⣿⣿⢷⣹⣹⣿⣷⡶⠏⠀⠀⡸⠀⢸⠀⠀⡏⡆⠀⢹⡀⠀
⠀⠀⡇⢠⠳⡜⣾⣿⡟⡇⠀⠀⠈⡆⢠⠿⣿⡿⢿⣿⣽⡷⢅⣻⠼⣩⠎⣿⣻⣼⣿⣿⡿⣿⣿⡗⠀⣀⠔⠁⠀⢸⠀⠀⡇⠸⡄⠀⠱⡀
⠀⠀⠉⠹⣣⣿⣼⡱⡏⠁⠀⠀⠀⠉⣽⣿⣿⣿⣾⣷⣿⣕⣯⣾⣭⣵⣿⠯⣝⡹⡩⢏⡵⢢⡓⢿⠉⠁⠀⠀⠀⠈⠉⠉⠁⠀⠉⠉⠉⠁
⢠⠤⠤⠴⣿⣿⣿⠗⠀⢠⠤⠤⢤⠀⢸⢟⡛⣛⣛⠻⣍⠾⣿⣷⡾⣿⡿⠳⣬⢱⡹⡜⡴⢣⡝⢎⠢⢤⡀⠀⠀⢠⠤⠤⠤⠤⢤⡀⠀⠀
⢸⣀⣀⠀⢈⣉⣸⠀⠀⡜⠀⠀⠘⡆⢘⠮⣜⡱⢎⡳⣌⠳⢦⡹⣿⣿⢇⡛⡴⢣⠳⣜⡱⢣⢎⡭⠀⠀⠙⢇⠀⢸⠀⠀⣀⡀⠀⠘⡆⠀
⠈⠀⢹⠀⢸⠈⠉⠀⢠⠃⠀⣇⠀⢳⣎⠞⡴⣙⠮⡱⢎⡝⢦⠳⣼⠉⡎⡵⣊⢧⢛⡴⣩⠓⡮⣼⠙⢆⠀⠘⡆⢸⠀⠀⡇⠈⡆⠀⡷⠀
⠀⠀⢸⠀⢸⠀⠀⠀⡞⠀⢸⢸⡀⠈⡇⠛⠴⢩⣖⡹⢎⣜⡣⠝⢸⠀⠈⡖⠛⠘⡳⠂⢱⠋⠀⠀⠀⢸⡄⠀⡇⢸⠀⠀⠓⠚⠀⢀⠇⠀
⠀⠀⢸⠀⢸⠀⠀⢸⠃⠀⠧⠦⠧⠀⢻⠀⠀⠀⡇⠀⢸⠀⠀⠀⢸⠀⠀⡇⠀⠀⢺⠀⠨⣇⠀⠀⠀⣸⠀⠀⡇⢸⠀⠀⣆⠀⠲⡉⠀⠀
⠀⠀⢸⠀⢸⠀⠀⡞⠀⢀⣤⣠⣀⡀⠈⡇⠀⠀⡇⠀⢸⠀⠀⠀⢸⠀⠀⠧⠤⢤⠘⣆⠀⠈⠒⠤⠚⠁⠀⡸⠁⢸⠀⠀⡏⣆⠀⠱⡄⠀
⡀⠀⢸⣀⣸⠀⢸⣁⣀⡏⠀⠀⠀⣇⣀⣸⡀⠀⣇⣀⣸⠀⠀⠀⢸⣀⣀⣀⣀⣸⠀⠈⠢⣀⡀⠀⢀⣠⠞⠁⠀⢸⣀⣀⡇⠘⣆⣀⣹⡄